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A219579 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array. 1

%I

%S 4,13,51,132,277,514,881,1429,2225,3355,4927,7074,9957,13768,18733,

%T 25115,33217,43385,56011,71536,90453,113310,140713,173329,211889,

%U 257191,310103,371566,442597,524292,617829,724471,845569,982565,1136995,1310492

%N Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array.

%C Row 2 of A219578.

%H R. H. Hardin, <a href="/A219579/b219579.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40)*n^5 - (5/24)*n^4 + (79/24)*n^3 - (91/24)*n^2 + (161/60)*n - 1 for n>1.

%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)

%F G.f.: x*(4 - 11*x + 33*x^2 - 59*x^3 + 50*x^4 - 17*x^5 + 3*x^6) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.

%F (End)

%e Some solutions for n=3:

%e ..2..0..0....1..0..0....1..0..0....3..2..2....3..2..2....2..0..0....2..2..1

%e ..2..1..0....2..1..0....1..1..0....3..3..2....3..2..2....3..1..0....2..1..1

%Y Cf. A219578.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2012

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Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)